*Not an official ACM page*

[Problem F
| 1994 Western European Regional problem set
| My ACM problem archive
| my home page]

#### 1994-1995 ACM International Collegiate Programming Contest

Western European Regional

Practice Session

# Problem E

## Rooks

Most people participating in the ACM scholastic programming contest have at some stage
been asked: 'Can you give an example of the type of problems you have to solve there?'. The
most common example selected in response is the 8-queens problem.
Of course, all of you have at one time or the other programmed the 8-queens problem.
So here is a small variation on that theme: determine the number of ways you can place *R*
rooks on an *R* × *R* chess board, such that no two rooks are on the same file or on the same rank.

### Input Specification

The first line of input contains an integer *N*, specifying the number of test cases. Each of the
*N* test cases consists of a single positive integer *R* (1 <= *R* <= 12) on a line by itself, indicating
which *R*-rooks problem you have to solve.
### Output Specification

For each test case, output the line '`There are `*S* solutions to the *R*-rooks problem.

',
where *S* is the number of solutions, and *R* is the size of the problem.
### Example Input

3
1
2
4

### Example Output

There are 1 solutions to the 1-rooks problem.
There are 2 solutions to the 2-rooks problem.
There are 24 solutions to the 4-rooks problem.

This page maintained by
Ed Karrels.

Last updated November 11, 1997